One of the reasons why conformal blocks appear in the construction of isomonodromic tau functions is that when the central charge takes particular values, monodromy invariant finite-systems can be constructed from conformal blocks with the degenerate field [1]}, [2]}. We note that by definition, local monodromies of conformal blocks are independent of their singular points, and connection problem of semi-degenerate \(W_N\) -conformal blocks with the degenerate field is reduced to connection problem of the Clausen–Thomae hypergeometric function \({}_{N}F_{N-1}\) . Recall that \(W_2\)  is the Virasoro algebra.
